Question 61 of 308

A particle of mass $m$ and charge $q$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed $v$ on the distance $x$ travelled by it is correctly given by (graphs are schematic and not drawn to scale)

ABCD

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Answer: (B)

The particle is at rest initially.
So, the initial velocity $u=0m{s}^{-1}$.
The force on the charged particle in the uniform electric field,
$F=qE$
$\Rightarrow ma=qE$
$\Rightarrow a=\dfrac{qE}{m}$
Applying the velocity-displacement equation under constant acceleration,
${v}^{2}={u}^{2}+2ax$
$\Rightarrow {v}^{2}={0}^{2}+2\left(\dfrac{qE}{m}\right)x$
$\Rightarrow {v}^{2}=\dfrac{2qE}{m}x$